$J$ $K$ $L$ If: $ JK = 4x + 8$, $ KL = 5x + 6$, and $ JL = 86$, Find $KL$.
Explanation: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {4x + 8} + {5x + 6} = {86}$ Combine like terms: $ 9x + 14 = {86}$ Subtract $14$ from both sides: $ 9x = 72$ Divide both sides by $9$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $KL$ $ KL = 5({8}) + 6$ Simplify: $ {KL = 40 + 6}$ Simplify to find ${KL}$ : $ {KL = 46}$